2019
Том 71
№ 8

# Lytvynov E. V.

Articles: 3
Brief Communications (English)

### The Jacobi Field of a Lévy Process

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 706-710

We derive an explicit formula for the Jacobi field that is acting in an extended Fock space and corresponds to an ( $\mathbb{R}$ -valued) Lévy process on a Riemannian manifold. The support of the measure of jumps in the Lévy–Khintchine representation for the Lévy process is supposed to have an infinite number of points. We characterize the gamma, Pascal, and Meixner processes as the only Lévy process whose Jacobi field leaves the set of finite continuous elements of the extended Fock space invariant.

Article (Russian)

### Spectral approach to white noise analysis

Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 177–197

By using the spectral projection theorem, we construct the classical Segal transformation as a Fourier transformation in the generalized joint eigenvectors of a certain family of field operators. It is noted that the spectral approach to the Segal transformation, which forms the basis of the analysis of Gaussian white noise, enables one to construct a significant generalization of this transformation.

Article (Ukrainian)

### On the existence of a cyclic vector for some families of operators

Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1362–1370